The quantum N-body problem with a minimal length

The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal observable length $\sqrt\beta$. For a generic pairwise interaction potential, analytical formulas are obtained that allow to estimate the ground-state energy of the $N$-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that, in the harmonic oscillator case, the $\beta$-dependent term grows faster with $N$ than the $\beta$-independent one. Then, it is argued that such a behavior should be observed also with generic potentials and for $D$-dimensional systems. In consequence, quantum $N$-body bound states might be interesting places to look at nontrivial manifestations of a minimal length since, the more particles are present, the more the system deviates from standard quantum mechanical predictions.Comment: To appear in PR

Covariant oscillator quark model for glueballs and baryons

An analytic resolution of the covariant oscillator quark model for a three-body system is presented. Our harmonic potential is a general quadratic potential which can simulate both a $\delta$-shape configuration or a simplified Y-configuration where the junction is located at the center of mass. The mass formulas obtained are used to compute glueball and baryon spectra. We show that the agreement with lattice and experimental data is correct if the Casimir scaling hypothesis is assumed. It is also argued that our model is compatible with pomeron and odderon approaches.Comment: 2 figures; content changed and enlarge

The quantum N-body problem and the auxiliary field method

Approximate analytical energy formulas for N-body relativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proved to be a powerful technique in the case of two-body problems. A general procedure is given and applied to various Hamiltonians of interest, in atomic and hadronic physics in particular. A test of formulas is performed for baryons described as a three-quark system.Comment: References adde

Auxiliary fields and the flux tube model

It is possible to eliminate exactly all the auxiliary fields (einbein fields) appearing in the rotating string Hamiltonian to obtain the classical equations of motion of the relativistic flux tube model. A clear interpretation can then be done for the characteristic variables of the rotating string model.Comment: No table, No figur

(2+1)(2+1)-dd Glueball Spectrum within a Constituent Picture

The quantum numbers and mass hierarchy of the glueballs observed in $(2+1)$-dimensional lattice QCD with gauge group SU($N_c$) are shown to be in agreement with a constituent picture. The agreement is maintained when going from glueballs to gluelumps, and when the gauge group SO($2N_c$) is taken instead of SU($N_c$)